RBE2 equations to establish the force distribution i.e. mpc forces?

[JBlack68]

To all,

Does anyone know a good source/ref for the equations used by (nastran) RBE2 element to get the load distribution assuming a force being applied at the independent node? I remember seeing something in the old msc.nastran manual but cannot find it anymore

If one was to set-up a simple RBE2 as follows;
[ul]
[li]Assume it only works in 1 direction-say vertical (Y)[/li]
[li]a load W is applied at the independent node[/li]
[/ul]

Would it be possible to write the equations in Mathcad to solve them?

Thanks
Regards

 

[rb1957]

I'd've thought that the rigid element proportions the reactions between the dependent nodes depending on the local stiffness at those nodes. (but that could be for RBE3).

If RBE2, I think this is a rigid element, so reactions can be calculated from the applied loads the the geometry of the dependent nodes, treating the dependent nodes as a bolt group.
1) calculate the CG of the dependent nodes.
2) determine the free body reactions at the CG.
3) proportion the direct loads equally between the dependent nodes.
4) react the CG moments, assuming plane sections remain plane. The issue is going to be if there are two loadpaths to react a moment; eg Mx can be reacted by Fy and Fz depending on the geometry. There probably is some virtual work principle that'll show the least work between the two loadpaths.

another day in paradise, or is paradise one day closer ?

 

[JBlack68]

I think there is a relation between translation (T) and rotation (R) (assumed very small)
{Tind} = {Tdep}+{R}{v} where v must be the vector defined by the position of the dependant and each independent node
If you consider an RBE3 with 3 dependant nodes working purely in 1 direction then If I got this right you only have 2 equations but 3 unknowns(the force at each dependant node one is seeking)

 

[rb1957]

yes, if the RBE is statically determinate then easy to solve.

if indeterminate, then "plane sections remain plane" allows us to solve ... the RBE is rigid so displacements of all points can be calculated from the induced deflection > strain > load.

another day in paradise, or is paradise one day closer ?

 

[JBlack68]

Ok so how does one establish the extra equation needed relating force et dish I guess
Small disp applies and rigid rotation

 

[rb1957]

rigid rotation ... if the element rotates 1deg about X axis (a unit Mx) what displacements occur at the dependent nodes, hence the load induced, hence the moment reacted. Then scale for required moment. repeat for other axes. add direct load.

another day in paradise, or is paradise one day closer ?